MCQ
The equivalent resistance of the infinite network given below is :
- A$2\,\Omega$
- B$(1+\sqrt{2})\,\Omega$
- ✓$(1+\sqrt{3})\,\Omega$
- D$(1+\sqrt{5})\,\Omega$
✓
Answer
Correct option: C.
$(1+\sqrt{3})\,\Omega$
c
If effective resistance is $x$,
If effective resistance is $x$,
$\Rightarrow x=1+\frac{x \times 1}{x+1}+1$
$\Rightarrow(x-2)=\frac{x}{x+1}$
$\Rightarrow x^2-x-2=x$
$\Rightarrow x^2-2 x-2=0$
$\text { So, } x=\frac{2 \pm \sqrt{12}}{2}$
$=1 \pm \sqrt{3}\,\Omega$
neglecting negative value, $x =1+\sqrt{3}\,\Omega$
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